Future aerospace missions increasingly operate in environments where nonlinear dynamics, tight performance constraints, and uncertainty are central design drivers. This workshop presents a unified framework for control under uncertainty, with direct application to spacecraft operating in cislunar space, close-proximity and formation missions, and hypersonic vehicles subject to severe state and control constraints.

In cislunar space, spacecraft motion is governed by multi-body gravitational dynamics that exhibit sensitive dependence on initial conditions and long-horizon instability. Trajectory design in this regime requires sophisticated numerical methods, while feedback stabilization near libration point orbits demands control laws that respect nonlinear structure and limited actuation. Uncertainty in ephemerides, environmental disturbances, and model mismatch further complicate mission design. Close-proximity operations introduce additional layers of complexity. Rendezvous, docking, on-orbit servicing, and formation flying must satisfy strict safety constraints, including collision avoidance, plume impingement limits, line-of-sight requirements, and actuator saturation. These missions demand trajectory planning methods that rigorously handle state and control constraints while maintaining robustness to estimation and modeling errors. Hypersonic vehicles present a different but equally challenging regime. Strong aerodynamic coupling, rapidly varying atmospheric conditions, thermal constraints, and limited control authority create tightly constrained, highly nonlinear control problems. Robust guidance and control architectures must account for parametric uncertainty, unmodeled dynamics, and state-dependent performance limitations.

This workshop develops unified perspectives that bridge trajectory optimization, nonlinear feedback design, stochastic optimal control, and adaptive control methodologies. Emphasis is placed on understanding how structure in optimal control problems including Hamiltonian formulations and value function geometry can be leveraged to design computationally tractable, robust controllers for safety-critical aerospace applications. By integrating numerical optimal control, dynamical systems theory, stochastic control, and adaptive methods, the session provides participants with conceptual and computational tools for addressing uncertainty within advanced aerospace vehicle guidance and control problems. At the end of the tutorial session, participants will be able to:

1. Formulate constrained nonlinear optimal control problems arising in cislunar spacecraft missions, proximity operations, and hypersonic flight.
2. Connect dynamical systems concepts and Hamilton–Jacobi theory to the synthesis of nonlinear feedback control policies.
3. Evaluate and design control strategies that explicitly account for parametric and non-parametric uncertainty using stochastic and adaptive control methods.
4. Integrate open-loop trajectory optimization with robust feedback design in safety-critical aerospace applications involving state and actuator constraints.
   
   

Abstracts for Talks:

Numerical Methods for Trajectory Planning: (Speaker: Maruthi Akella and Puneet Singla)
The session will begin with fundamental principles of indirect optimal control, emphasizing state-of-the-art numerical techniques for solving two-point boundary value problems. Both classical formulations and modern computational strategies will be discussed, with attention to practical implementation challenges. The application of these methods to design ballistic trajectories for space vehicles in multi-body environment and trajectory planning for high-speed vehicles under state and control constraints will be demonstrated.

Dynamic System Theory for Optimal Feedback Control (Speaker: Roshan Eapen)
This session will explore the deep connections between dynamical systems theory and optimal feedback control. Leveraging Hamilton–Jacobi theory, we will examine how optimal control policies emerge from canonical transformations and discuss implications for nonlinear model predictive control.

Adaptive Control (Speaker: Maruthi Akella)
This Session will address control under uncertainty, covering both stochastic optimal control and adaptive control methodologies. Approaches for handling parametric and non-parametric uncertainty will be presented, along with insights into robustness and learning-based adaptation.